3.3 Two-shock approximation for relativistic 3 High-Resolution Shock-Capturing Methods3.1 Relativistic PPM

3.2 The relativistic Glimm method 

Wen et al. [187Jump To The Next Citation Point In The Article] have extended Glimm's random choice method [65] to 1D SRHD. They developed a first-order accurate hydrodynamic code combining Glimm's method (using an exact Riemann solver) with standard finite difference schemes.

In the random choice method, given two adjacent states, tex2html_wrap_inline5927 and tex2html_wrap_inline5929, at time tex2html_wrap_inline5931, the value of the numerical solution at time tex2html_wrap_inline5933 and position tex2html_wrap_inline5935 is given by the exact solution tex2html_wrap_inline5937 of the Riemann problem evaluated at a randomly chosen point inside zone (j, j +1), i.e.,

equation364

where tex2html_wrap_inline5941 is a random number in the interval [0,1].

Besides being conservative on average, the main advantages of Glimm's method are that it produces both completely sharp shocks and contact discontinuities, and that it is free of diffusion and dispersion errors.

Chorin [29] applied Glimm's method to the numerical solution of homogeneous hyperbolic conservation laws. Colella [31Jump To The Next Citation Point In The Article] proposed an accurate procedure of randomly sampling the solution of local Riemann problems and investigated the extension of Glimm's method to two dimensions using operator splitting methods.



3.3 Two-shock approximation for relativistic 3 High-Resolution Shock-Capturing Methods3.1 Relativistic PPM

image Numerical Hydrodynamics in Special Relativity
Jose Maria Martí and Ewald Müller
http://www.livingreviews.org/lrr-1999-3
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